Sunday, October 22, 2006

Orbital radii of exoplanets and Bohr quantization of planetary orbits

Orbital radii of exoplanets save as a test for the Bohr quantization of planetary orbits. Hundreds of them are already known and in tables (Masses and Orbital Characteristics of Extrasolar Planets using stellar masses derived from Hipparcos, metalicity, and stellar evolution) basic data for for 136 exoplanets are listed. The tables also provide references and links to sources giving data about the stars, in particular star mass M using solar mass MS as a unit. Hence one can test the formula for the orbital radii given by the expression

r/rE= (n2/52) ×(M/MS)× X ,

X= (n1/n2)2, ni=2ki× ∏siFsi ,

Fsi in the set {3,5,17,257, 216+1} . Here a given Fermat prime Fsi can appear only once.

It turns out that the simplest option assuming X=1 fails badly for some planets: the resulting deviations of of order 20 per cent typically but in the worst cases the predicted radius is by factor of ≈ .5 too small. The values of X used in the fit correspond to X having values in {(2/3)2, (3/4)2, (4/5)2, (5/6)2, (15/17)2, (15/16)2, (16/17)2} ≈ {.44, .56,.64,.69,.78, .88,.89} and their inverses. The tables summarizing the resulting fit using both X=1 and X giving optimal fit are here. The deviations are typically few per cent and one must also take into account the fact that the masses of stars are deduced theoretically using the spectral data from star models. I am not able to form an opinion about the real error bars related to the masses.

The appendix of the chapter TGD and Astrophysics of "Classical Physics in Many-Sheeted Space-Time" contains more details.

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